Nellie's Nachos is a fast food restaurant chain that has locations in many cities throughout the United States. In one Nellie's Nachos restaurant located on the west coast, the average number of customers served per day is 330 330 with a standard deviation of 45 45. In one Nellie's Nachos restaurant located on the east coast, the average number of customers served per day is 315 315 with a standard deviation of 60 60. Assume the distribution of the number of customers served per day is approximately normal at both locations. Also assume that the number of customers served at one store is independent of the number of customers served at the other store. What is the probability that on one randomly selected day, the number of customers served in the east coast location is greater than the number of customers served in the west coast location? A) 0.1587 B) 0.3527 C) 0.4207 D) 0.5 E) 0.5793
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Nellie's Nachos is a fast food restaurant chain that has locations in many cities throughout the United States. In one Nellie's Nachos restaurant located on the west coast, the average number of customers served per day is 330 330 with a standard deviation of 45 45. In one Nellie's Nachos restaurant located on the east coast, the average number of customers served per day is 315 315 with a standard deviation of 60 60. Assume the distribution of the number of customers served per day is approximately normal at both locations. Also assume that the number of customers served at one store is independent of the number of customers served at the other store. What is the probability that on one randomly selected day, the number of customers served in the east coast location is greater than the number of customers served in the west coast location?
A) 0.1587
B) 0.3527
C) 0.4207
D) 0.5
E) 0.5793
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